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Express x^2-7x+2 in the form (x-p)^2+q where p and q are rational. Hence or otherwise find the minimum value of x^2-7x+2

For the first part, use the 'complete the square method', which gives (x-7/2)²-49/4+2, simplified to (x-7/2)²-41/4. To find the answer for the second part, set x=7/2 so that the bra...

Answered by Connaire W. • Maths tutor

4332 Views

Find the binomial expansion of (2+x)^3

We know thst the binomial expansion formula is (1+x)ⁿ= 1+nx +(n)(n-1)(x²)/2! ...etc

Thus we want to rearrange the expression we are given into the form (1+x)ⁿso t...

Answered by Laura V. • Maths tutor

8150 Views

Given that y = 3x(^2) + 6x(^1/3) + (2x(^3) - 7)/(3(sqrt(x))) when x > 0 find dy/dx

Firstly, the (2x(^3) - 7)/(3(sqrt(x))) can be split into (2x(^3))/(3(sqrt(x)) and -7/(3(sqrt(x)). These can then be simplified to (2/3)x(^5/2) and -(7/3)x(^-1/2) respectively. This then gives the equation...

Answered by Samuel H. • Maths tutor

15938 Views

Solve the following simultaneous equations: 3a + 2b = 36 equation ( 1), and 5a + 4b = 64 equation (2)

This question can be answered by the elimination method, substitution method or graphically. I find the elimination method easiest, especially when you can see that the coefficient of a variable (in this ...

Answered by Alejandro G. • Maths tutor

5168 Views

There are 30 kg of potatoes in a wheelbarrow. A farmer adds some carrots into the wheelbarrow. The total weight of the wheelbarrow now is 110 pounds. What weight of carrots did the farmer put into the wheelbarrow? 1 kg = 2.2 pounds

First of all, you want to get all your data in the same units, so either in pounds or kg. Here, as you are told that 1kg = 2.2 pounds, it seems easier to convert the amount of potatoes from 30kg into poun...

Answered by Alejandro G. • Maths tutor

4364 Views